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課程名稱 |
微積分甲上
Calculus (general Mathematics) (a)(1) |
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開課學期 |
102-1 |
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授課對象 |
電機工程學系 |
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授課教師 |
顏文明 |
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課號 |
MATH1201 |
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課程識別碼 |
201 101A1 |
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班次 |
02 |
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學分 |
4 |
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全/半年 |
全年 |
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必/選修 |
必修 |
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上課時間 |
星期一9(16:30~17:20)星期三5,6(12:20~14:10)星期五5,6(12:20~14:10) |
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上課地點 |
新203新203新203 |
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備註 |
統一教學.大二以上限20人.一9為實習課.
限本系所學生(含輔系、雙修生)
總人數上限：130人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1021A02 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
http://www.math.ntu.edu.tw/~mathcal/download/991/991A1.pdf |
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課程目標 |
Study the process of approximation and its limitation (errors), learn the tools and techniques for analyzing regular mappings with applications, and deepen the understanding of elementary functions. |
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課程要求 |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
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參考書目 |
James Stewart, Calculus Early Transcendentals, 7th edition. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Midterm Exam |
40% |
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2. |
Homework and Quiz |
20% |
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3. |
Final Exam |
40% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/11,9/13 |
[1.5] Exponential Functions
[1.6] Inverse Functions and Logarithms
[2.1] The Tangent and Velocity Problems
[2.2] The Limit of a Function
[2.3] Calculating Limits Using the Limit Laws |
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第2週 |
9/18,9/20 |
[2.4] The Precise Definition of a Limit
[2.5] Continuity |
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第3週 |
9/25,9/27 |
[2.6] Limits at Infinity; Horizontal Asymptotes
[2.7] Derivatives and
Rates of Change
[2.8] The Derivative as a Function
[3.1] Derivatives of Polynomials and Exponential Functions |
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第4週 |
10/02,10/04 |
[3.2] The Product and Quotient Rules
[3.3] Derivatives of Trigonometric Functions
[3.4] The
Chain Rule
[3.5] Implicit Differentiation |
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第5週 |
10/09,10/11 |
[3.6] Derivatives of Logarithmic Functions
[3.7] Rates of Change in the Natural and Social Sciences
（
※
）
[3.8] Exponential Growth and Decay
[3.9] Related Rates
[3.10] Linear Approximations and
Differentials
[3.11] Hyperbolic Functions |
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第6週 |
10/16,10/18 |
[4.1] Maximum and Minimum Values
[4.2] The Mean Value Theorem |
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第7週 |
10/23,10/25 |
4.3] How Derivatives Affect the Shape of a Graph
[4.4] Indeterminate
Forms and L’Hospital’s Rule
[4.5] Summary of Curve Sketching
[4.6] Graphing with Calculus and Calculators
（
※
）
[4.7] Optimization Problems |
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第8週 |
10/30,11/1 |
[4.8] Newton’s Method
（
※
）
[4.9] Antiderivatives
[5.1] Areas and Distances |
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第9週 |
11/06,11/08 |
[5.2] The Definite Integral
[5.3] The Fundamental Theorem of Calculus
[5.4] Indefinite Integrals and the Net Change Theorem
[5.5] The Substitution Rule |
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第10週 |
11/13,11/15 |
[6.1] Areas
Between Curves
[6.2] Volumes
[6.3] Volumes by Cylindrical Shells
[6.4] Work
（
※
） |
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第11週 |
11/20,11/22 |
[6.5] Average Value of a Function
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※
）
[7.1] Integration by Parts
[7.2] Trigonometric
Integrals
[7.3] Trigonometric Substitution
[7.4] Integration of Rational Functions by Partial Fractions |
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第12週 |
11/27,11/29 |
[7.5] Strategy for Integration
[7.7] Approximate Integration
[7.8] Improper Integrals
[8.1] Arc Length |
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第13週 |
12/04,12/06 |
[8.2] Area of a Surface of Revolution
[8.
3
] A
pplications to Physics and Engineering
[8.
4
]
Applications to Economics and Biology
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※
）
[8.
5
]
Probability
（
※
） |
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第14週 |
12/11,12/13 |
[9.1]
Modeling with Differential Equations
[9.2] Direction Fields and Euler’s Method
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※
）
[9.3] Separable Equations
[9.4] Models for Population Growt |
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第15週 |
12/18,12/20 |
[9.5] Linear Equations |
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第16週 |
12/25,10/27 |
[10.1] Curves Defined by Parametric Equations
[10.2] Calculus with Parametric Curves
[10.3] Polar Coordinates
[10.4] Areas and Lengths in Polar Coordinates
[
10.6
]
Conic Sections in Polar Coordinates |
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